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arXiv · 1306.0224

q-symmetric functions and q-quasisymmetric functions

Yunnan Li
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Abstract

In this paper, we construct the q-analogue of Poirier-Reutenauer algebras, related deeply with other q-combinatorial Hopf algebras. As an application, we use them to realize the odd Schur functions defined in \cite{EK}, and naturally obtain the odd Littlewood-Richardson rule concerned in \cite{Ell}. Moreover, we construct the refinement of the odd Schur functions, called odd quasisymmetric Schur functions, parallel to the consideration in \cite{HLMW1}. All the q-Hopf algebras we discuss here provide the corresponding q-dual graded graphs in the sense of \cite{BLL}.

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Yunnan Li. 2013-06-02. q-symmetric functions and q-quasisymmetric functions. https://arxiv.org/abs/1306.0224

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